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What are the complete assumptions and final conclusions from 'Thin Airfoil Theory' in aerodynamics?
I possess expertise in the field of aerospace structures, however I have recently been assigned an 'Aeroelasticity' analysis job at my workplace. In an effort to imbibe the fundamental knowledge which'd lead me to execute my gig in a proper way, I came across the concept of 'Thin Airfoil'.
Although I realized that mutitude of books addresses the mathematical derivation of aerodynamic parameters and coefficients by engaging this thin airfoil concept, but I couldn't still wrap my head around the basic reasons why exactly would we need to introduce this concept and in what way does it emerge favorable for the engineers? What is the complete set of assumptions and the final conclusions which are derived through this theory? Can I reach to similar conclusions and equations if I shy away from employing this concept? Do the real-world airfoils and wings behave exactly in the same fashion as predicted by this theory? What do I gain and where exactly do I compromise in all this?

Thin airfoil theory is based on a laundry list of assumptions -- I may miss some, but here are the big three...

Inviscid flow (flow without viscosity / friction)

Incompressible flow (fluid medium is incompressible, i.e. liquid, or if a gas, you are near the low Mach number limit where compressibility is not important)

Small disturbance, small angles, and the general assumptions that go along with linearizing the governing equations.

Thin airfoil theory was developed during a very active time of aerodynamics (1900-1930 ish).  It was the first theory that could do a good job modeling arbitrary airfoils (not just very special cases).  Thick airfoil theories would come later -- many of which would only be practical with digital computers.
The main competing theory of the time was 'conformal theory'.  I.e. complex analysis (using $\sqrt{-1}$) was used to transform an airfoil into a shape with a known analytical solution (a circle).  Different transformations would allow different airfoil-like shapes -- and would thereby provide 'exact' solutions for those airfoils.  Unfortunately, you could not transform any shape, only those for which a transformation had been discovered/derived.  This would prove to not be very practical for engineering use (though is powerful as a test/check of other methods).
The important thing about conformal theory is that it too relied on 1) and 2) above -- as did the thick airfoil theories that would come soon thereafter.
All of these 2D airfoil theories suffer from d'Alembert's paradox -- theory predicts zero drag on an airfoil, but observation of real airfoils exhibit finite (non-zero) drag.  This is due to their ignoring viscoscity.
Boundary layer theory (simple treatment of friction) was developing at the same time, but it was only applied to flat plates at the time -- it would not be applied to airfoils until later and then typically with very cumbersome computations or a modern computer.
Non-incompressible theories (subsonic, supersonic, and eventually transonic) would come along, but would mostly require modern computers.
All that is to say that the unique part of thin airfoil theory was the assumptions from 3), not so much 1) & 2) (as all competing options had the same limitations for some time).
The important outcome of thin airfoil theory is that an airfoil can be decomposed into three flows that can be analyzed separately, but added together (through superposition) to model the complete flow.  These three flows are:
A) a thin flat plate at an angle of attack
B) a thin curved surface representing the mean camber line
C) a symmetrical thickness form
A) tells us that the lift curve slope of an airfoil is $2\pi$ per radian (0.1097 per degree) and the aerodynamic center is at the quarter-chord (c/4).
B) tells us that the camber form determines the zero-lift angle of attack, the design lift coefficient, and the zero lift pitching moment coefficient.  This can also be used to calculate the load distribution for a given camber line.  Importantly, this step can also be inverted -- starting with a desired load distribution, we can calculate the shape of the mean camber line.  This enabled practical airfoil design -- not just analysis.
C) tells us how much the flow accelerates around the airfoil due to the thickness (not just the production of lift).  I.e. it will inform the magnitude of the supervelocities around the top and bottom surface, but the resulting pressures cancel out in terms of creating forces.  We will be able to design good thickness families (in terms of promoting laminar flow, or delaying compressible drag rise) and then apply those to various camber lines to construct families of designed airfoils.
The approximations introduced by the linearization (3) above) are really quite reasonable in most situations.  In practice, thin airfoil theory does a very good job up to pretty thick airfoils.
There are more implications of the use of superposition.  We can further use superposition when designing the mean camber line -- two camber lines (say one curved at the front, and one curved aft) can be combined through superposition to achieve a complex camber line with curvature at the front and back.
This principle of aerodynamic superposition is fundamental to aeroelasticity.
First, we will use a similar set of assumptions for the structural model -- we will use linear elasticity theory.  This limits us to small disturbances, but it also allows us to use superposition on the structure -- if we calculate the deflected shape of load distribution 1 and 2, we find that the deflected shape of load 1+2 is the sum of the deflected shapes.  This idea is central to the development of finite element analysis.
In aeroelasticity, we typically start by finding the natural mode shapes of the structure (from eigen analysis).  We then force the aerodynamic tool to model a structure deflecting in that mode shape (first bending, first twisting, second bending, etc).  This aerodynamic tool gives us the distribution of pressure increments due to the specified deflection shape.
Just as complex deflections can be formed by superposition of the natural mode shapes, we can calculate the aerodynamic force on a complex deflected shape by superposition of the force due to the natural deflections.
In aeroelasticity, we form a 2nd order ODE -- a spring-mass-damper problem -- in matrix form.
The stiffness matrix is the stiffness matrix from the FEA analysis.  The mass matrix is usually the identity matrix (as a result of using the natural modes as our deflections).  The damping matrix comes from the aerodynamic tool.
The siffness provides the forces in response to the deflections.
The mass provides the forces in response to the accelerations.
the damping provides the forces in response to the rate of the deflections.
You then perform linear stability analysis on this ODE to determine the conditions (typically airspeed) at which it goes unstable (flutter boundary).
Obviously there is a lot more to aeroelasticity, but at this point, I think you can see that the linearization and superposition in thin airfoil theory are fundamental building blocks in the foundation of aeroelasticity.

Are we comprimising on the accuracy of any parameters or coefficients drawn out of the application of thin airfoil theory? Do all the airfoils and wings always behave in the same as being predicted by this theory, or is there a range?

Every model is approximate.  Whether thin airfoil theory is valid depends on both the geometry and flow condition -- for the most part, reasonable airfoil geometries are OK.  TAT does not work when the airfoil approaches stall.  It also breaks down in transonic flow.  However, the important conclusion from TAT is superposition (which is used in almost all aeroelasticity analysis) still holds in many cases where you would not trust TAT.  We would really need to know more about your problem and other tools to judge the role of TAT -- it probably isn't the weak link in this chain.

What are the complete assumptions?

Fluid is:

irrotational;
incompressible and;
inviscid.

Under these hypothesis the full Navier-Stokes equations of the fluid dynamics reduce to the simple Laplace's equation:
$\nabla ² \phi=0$.
The Laplace equation is one of the most studied linear partial differential equation since it describes many natural physical phenomena. Knowing the boundary conditions, it can be univocally solved. Being linear, a solution for a complex phenomenon can be obtained summing up several basics solutions.
For an aerodynamic problem the boundary conditions are:
a. velocity is constant at infinity;
b. velocity is zero perpendicularly to the aerodynamic surface (so called non-penetration condition).
The thin airfoil condition introduces two additional simplifications to the problem:

the airflow is bidimensional;
the airfoil is thin, i.e. the chord is much bigger than the thickness.

Under these additional simplifications both $\phi$ and the boundary condition b. can be expanded as Taylor series and only the first two terms (zeroth-order and first-order) can be kept to do the math and solve the problem.
Due to 1., 2. and 3. Bernoulli's equation applies as well and the aerodynamic characteristics of the airfoil (lift and pitching moment) can be relatively simple solved by hand... and that's why it was introduced in the first place: before any computer was there, the thin airfoil theory provided a method to solve complex aerodynamic problems by hand.

What are the... final conclusions?

Any thin airfoil can be seen as the sum of:

a flat plate at a certain angle of attack $\alpha$; this is the zeroth-order solution from the Taylor series;
a cambered plate at zero $\alpha$; this is the first-order contribution.

Given the mathematical description of the camber, the aerodynamic lift and pitching moment can be calculated. In particular:

lift $\rightarrow$ lift due to the zeroth-order (flat plate) is $C_{l_0}=2π\alpha$; lift due to the first-order (camber) depends on the exact equation of the camber but the biggest contribution to the lift comes from the backward part of the airfoil: that's why ailerons, flaps and other moving surfaces are normally located in the last 20% of the chord toward the trailing edge.

moment $\rightarrow$ if the moment is calculated in respect to the point located at 1/4 of the chord (aerodynamic center) then it doesn't change with $\alpha$ i.e. the contribution due to the zeroth-order is null and only the first-order (camber) contributes to the pitching moment.

Navier-Stokes, but too small of an edit for my rep.

@OrganicMarble done, thanks

"fluids are … incomprehensible" – Isn't that the assumption of every engineering student?

@JörgWMittag: of many spelling checker as well

A word of caution-- it doesn't appear to me that the edit history of this answer is substantially different in nature from the edit history of this question, which got locked, presumably due to excessive editing-- https://aviation.stackexchange.com/posts/98210/revisions

@quietflyer: I suppose you're commenting under the wrong answer.


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What happens to Lift and Drag on aircraft (and its components) when sideslip is increased gradually from 0 degrees to 90 degrees?
I possess an Aerospace Engineering background, and work as a Aerospace structural analyst at a local firm. A portion of my job is dedicated to determining the critical conditions that the aircraft and its component can undergo, and then conduct Finite Element Analysis for those components under these limiting loading conditions. Before jumping onto the CFD team (to acquire the loads), I first have to make up my mind what conditions I reckon should return me critical loads acting on the aircraft.
I usually make use of V-N diagrams to deduce which are the most critical loadings on my civil aircraft, beyond which the structure is deemed to have failed. However, the V-N diagrams for an aircraft don't include the Sideslip effect. I am not a CFD specialist, so I don't know what would be the response of the aircraft (and its components) when subjected to wind at a certain sideslip angle.
Assume, I am currently working on the fuselage component of my civil aircraft, and want to obtain the most critical loads which can possibly act on it while in flight. So how would the sideslip play a role in this scenerio? What happens to the lift and drag values as the sideslip angle keeps on increasing gradually from 0 degrees to 90 degrees, in flight? What pattern would the lift and drag follow during this period? Should this pattern be the same for all components of the aircraft (like fuselage, wing, tail, etc) or it can be different?

That's a huge question.

Don't forget to consider "sideforce" as well-- "sideways" lift generated by sideslip-- acting  orthogonal to the flight path and free-stream relative wind, and also orthogonal to the lift vector.

Honestly I think the problem has to be tacked by a CFD model including the entire aircraft.  Probably shouldn't have tried to answer at all, just wanted to point out that yes definite elements of the aircraft will definitely respond differently.

@quietflyer, I totally agree with you. Conducting a CFD and then observing the results would be the most feasible approach here. But just picking those conditons from the CFD where the aircraft (or its individual components) are experiencing the highest or most critical loads and then directly interpolating those loads onto the concerned structure in my FEA model, is something which I don't prefer, unless I know why it is happening, so that it will save me some time in the future if I encounter similar problems.

Plus, sometimes the CFD results are not available for each and every possible condition, and you have to pick some points where you think the critical loads should appear for each part of the aircraft, so understanding and absorbing the concept goes a long way there. But I appreciate your effort in trying to help, thanks.

Good question. Quick comment: the team that supplies pressures can be the Aero (CFD) folks, but the team that defines "critical load conditions" are the Flight Loads folks. FL team uses flight dynamics simulations (tons of them) to determine critical load conditions for the whole airframe (and its components). Simulations include on-ground side winds, all flight regime and failure cases. If an airplane has 90 deg sideslip "in flight" it's possibly hovering (or falling).

I don't know what would be the response of the aircraft (and its components) when subjected to wind at a certain sideslip angle.

Obviously you understand that "sideslip" just means "sideways wind".  The nose is pointing at non-zero yaw angle (or more properly "slip angle") relative to the direction of the flight path and the free-stream relative wind, so the airflow is hitting the side of the aircraft.

What pattern would the lift and drag follow during this period? Should
this pattern be the same for all components of the aircraft (like
fuselage, wing, tail, etc) or it can be different?

Well, that part's easy.  It will be dramatically different.  Say you start increasing sideslip angle more and more, so the nose is pointing to left of the flight path.
If aircraft has dihedral, the right wing will experience an increase in lift.  The left wing will experience a decrease in lift.  The overall total lift vector is bound to decrease to some degree, especially at extreme slip angles.  The overall drag vector of the wing may not change hugely, but the more the dihedral (or anhedral), the more the sideways wind will generate some extra drag.
The fuselage (and vertical fin) will see a huge increase in drag which may reach maximum at 90 degrees slip angle.  The fuselage (and especially vertical fin) will also generate a "sideforce" component-- "sideways lift", acting orthogonal to the flight path and free-stream relative wind and also orthogonal to the aircraft's "vertical" axis or yaw axis.  In other, words also generally orthogonal to the overall lift vector of both wings combined.  This "sideforce" from the fuselage and fin will peak long before the sideslip angle reaches 90 degrees-- likely well before the sideslip angle even reaches 45 degrees, and then will start to decrease again, and may be zero when the sideslip angle reaches 90 degrees.
Does that help get you started?
It sounds like you've got an enormous task ahead of yourself here.

I am guessing you are aware of the role in V-N diagrams in aerospace structures. It guides and informs us the limiting loads (or to be more precise, the limiting aircraft lift) that it can see during flight operations. But it doesn't include the effect of sideslip angle, atleast I haven't seen a V-N diagram having so. So how does the aircraft manufacturing companies figure out the V-N diagrams (and the respective limiting alpha and sideslip angles of the aircraft, for example at a 4g maneuver) if sideslip effects are also taken into account?

Re -"So how does the aircraft manufacturing companies figure out the V-N diagrams (and the respective limiting alpha and sideslip angles of the aircraft, for example at a 4g maneuver) if sideslip effects are also taken into account? "-- honestly I would guess that they often don't.  And certainly not at really extreme sideslip angles like approaching 90 degrees.  But maybe someone better qualified will post an answer.  Maybe consider posting another question simply asking if loading from sideslip is taken into account, and if so, typically up to what sorts of sideslip angles?

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Do fighter jets experience angles of attack greater than stall when initiating a zoom climb?
I was just wondering that the fighter jets like F-16, F-35 and Rafale when they are doing a steady flight at a certain airspeed, try to rotate 90 degrees and aim to obtain a vertical motion, so does the angle of attack during this maneuver crosses the stall angle on these fighter jets or not?
Since by definition, angle of attack means the angle between the incoming airflow and the aircraft wing chord line, so I don't know if this changes (or goes beyond the stall angle) during this maneuver.
Even if it goes beyond the stall angle, can it still create a problem for the fighter jet (because I heard that the high Thrust/Weight ratio allows the fighter jets to do these unusual and extreme maneuvers without causing it to stall).

Comments are not for extended discussion; this conversation has been moved to chat.

The answer depends on two factors - aircraft speed, and pitch rate.  There are virtually infinite combinations of these two variables, but let's consider four for the sake of discussion:

Low speed, slow pitch rate - Done in a controlled manner, a fighter with a better than 1:1 thrust to weight ratio can rotate smoothly to vertical without exceeding stalling AOA, light the burners, and accelerate upwards.  The Blue Angels do a quasi-demonstration of this during their airshows.

Low speed, fast pitch rate - This is where stalling AOA can be easily exceeded, and a rather violent departure from controlled flight may result.  To be avoided.

High speed, slow pitch rate - An airplane with sufficient kinetic energy can arc gracefully into the vertical in a zoom climb, trading excess airspeed for altitude.  Thrust to weight ratio has nothing to do with it since gliders are capable of this.  However, the better the thrust weight ratio the longer you can sustain the climb.

High speed, fast pitch rate - This is where in the high speed portion of the performance envelope, (above cornering speed) you would exceed the max G limits of the aircraft before you reach a stalling AOA.

A good fighter pilot understands the energy state of the aircraft as well as the performance envelope, and can manage both to achieve maximum performance.  But there isn't a single correct answer to the basic question.

Sorry that I could only give you one upvote.

Great answer. For the 1st and 2nd cases (i.e. low speed), after the aircraft reaches the vertical position, now the speed of motion towards the sky will be different (I guess much more higher) than at what it was turning, right? Since now the thrust has to play an important role in overcoming the weight of aircraft.

Moreover, the G limits can also be exceeded for 3rd as well, right?

@RameezUlHaq, Thanks, and yes - extreme thrust is required to recover from 1 & 2.  Any airplane other than a high performance fighter will mush into a stall.  I know these two scenarios are not what you were asking, but I felt it was worth bringing them up to define the corners of the "box".  You could exceed G limits in #3 because of the speed, but not if you are careful and pitch slowly.  Again, there are infinite combinations of speed, thrust setting, and pitch rate available to a pilot...

@MichaelHall, basically what we know is that if you want to speed up your aircraft then you need to decrease your A.o.A, otherwise the aircraft can exceed its max G-limits. Now, you said the fighter jets speed up for the 3rd case. I was thinking that the pitch is slow, yes, but is in such a controlled manner that it causes the A.o.A to decrease while coming in the zoom climb mood, so that the G-limits are not exceeded. What would you say?

@RameezUlHaq, I’m not sure where your confusion lies, but I would say that you are looking at this the wrong way:  The only way to decrease AOA in a zoom climb from horizontal to vertical flight is if you started out inverted.  If you start out upright, you MUST increase AOA and Gs as you pitch the nose up to climb.  And you can be quite aggressive in doing so without exceeding limits.

Pitching the nose up in a slow and controlled manner basically means that we are trying to control the A.o.A, right? So that it just doesn't increase dramatically and cause the G-Limits to be exceeded all of a sudden, right?

@RameezUlHaq, yes, if “decreasing AOA” in a climb just means “use less than what will overstress the airframe”.  But the way you describe it sounds like you need to be extra cautious.  You can fly a fighter very aggressively and not exceed G limits as long as you have some awareness and know what you are doing.

An examination of a typical flight envelope may leave one wondering about exceeding G limits, rather than stalling.  A zoom climb typically starts by gaining as much kinetic energy as possible (speed) before turning sharply skyward. As excess drag would result in a lower, slower climb, stalls would be strictly avoided.
At high speeds one would pull the stick to climb, experiencing crushing G's long before stall.  The pilot's ability to withstand the G's would be the limiting factor in a fighter jet, followed by the G loading limits of the aircraft itself.
Unless trying to complete a loop at a much lower airspeed, high AoA's will likely overstress the pilot/aircraft well before stall.

so you are saying the aircraft will not experience stall during this transition?

If it is going very fast it will exceed G loads first.

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Does use of flaps or ailerons affect the aerodynamic forces distribution on the wing area before them?
Assume I want to use the flaps or ailerons at a specific altitude for some maneuevers on an aircraft. We know that the overall aerodynamic forces like lift and drag on an aircraft wing will change values when these control surfaces are used, but the use of these surfaces will also cause a change in the lift/drag distribution on the wing region/area which is located before these control surfaces or not?
I mean the change in the net aerodynamic forces on a wing only result from the usage of these control surfaces, or the force/drag distribution on the immovable wing parts also change and also contribute to the overall change in the lift and drag forces for that wing?

Are you interested just in theory, "how it happens"? Then you have an answer already (for subsonic speeds, the entire surface is affected; for supersonic speeds, not). But if you are concerned about how to calculate/find it, then the standard aerodynamic data already takes whatever happens into account. In many cases you'll have some additive quantities like, say, $\Delta C_L = 0.05$ per degree of deployment, and if you only need to know the net effect of (say) flaps, you just use these data, without the need to recalculate it for the "whole wing".

This shows the chordwise pressure distribution of a typical airfoil with a slotted flap retracted, at 10, 20 and 30deg, at both constant lift and at constant angle of attack. Deploying flaps changes the lift distribution across the entire chord of the wing. Ailerons have the same effect.

An important qualification to this answer would be "only for subsonic speeds".


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How to calculate Night Flight time for a given flight?
I am currently working on a project (web app) at university to be able to calculate the amount of time spent during night flying. Currently, I have,  Departure Lat and Long and Departure Time in UTC  Arrival Lat and Long and Arrival Time in UTC Sunset and  Sunrise Times (Based on dates) for both Arrival and Departure airfields in UTC
An example:  Depart UK Edingburgh airport on the 23 April 2019 at 11:10 UTC  Arrive Riyadh Airport at 18:10 UTC Total Time 7hr  day flight = ?  night flight = ?
I know many places online do this type of calculation for you, so I am wondering if there is a formula or method available that allows me to do this calculation (Which I can then convert to code)?
Thanks

Hello, @Bianfable, this isnt quite what I was looking of, am looking for a more mathematic calculation, but thank you

If you are more interested in the maths rather than the aviation aspect, you might get a better answer at Geographic Information Systems.

Before you can get to the math, you need to figure out what “night” means. Every country has their own definition, and some have more than one. And they’re all different. It is entirely possible that a flight changes from day to night or vice versa simply because you crossed a border.

For that, I will base it on EASA guidance but for now, for simplicity, I will just assume between sunset and sunrise

Welcome to aviation.SE! I suggest you check out this article on how it's implemented in a popular online logbook. The code is also on github.

This answer will address your question according to US FAA guidelines. Make sure to verify with your country’s aviation agency.
Civil Twlight
The time that you can log as “night” is based on the start or end of “civil twilight.” Civil twilight is defined as the time when the geometric center of the Sun’s disk is at most 6 degrees below the horizon. Civil twilight, as a general rule, is usually the 30 minutes before sunrise or after sunset. However, that can vary quite a bit with your location on the Earth’s surface.
Logged Time
Before (morning) or after (evening) civil twilight and between the two is when you can log night flight. You can take your total time (ie 2.3 Hobbs) and subtract any time that would not count as night and the result is what you are legally allowed to log as night time (at least here in the US).
Application for Development
I understand you're problem as a developer - you will have to use a website like timeanddate.com to grab an API that can find a local civil twlight using a city as an input. You will have to write a function that takes the departure time and determines whether it counts as night time, and then subtract any flight time that is ineligible.
I hope this addressed the mathematical request of your question and let me know if I can clarify at all.

That great thanks,
But referring to the example above, say we depart in the day and are flying W->E, then at what point during that flight would we hit night?

I would clarify by saying that when the time in whatever local time zone you are in is classified as night by the criteria above, you can determine that your flight is now flying under “night” logging.

@AkshayPatel Night time is not based on departure time or arrival time, it is calculated on the basis of what portion of the flight was flown at a time within civil twilight time for a particular location. Depending on what type of aircraft you are flying, it is possible to fly nonstop for 24 hours and not be able to log night time.

@JuanJimenez , this I understand and that is why I am trying to calculate at what point of flight would hit defined night  (If traveling East to West and you take off in the day) you may eventually catch the night  (Assuming constant speed)
(If that makes sense?)

The answer to your question depends on many factors that you have not expressed, such as speed, time of departure, flight route, etc. To my mind, as a programmer, it would make more sense to sample the location of the aircraft and local time at defined intervals to decide if the flight is currently within local civil twilight time at that location.

Thanks @JuanJimenez ,
I think I am getting there, so far I am plotting a GC course and then with the initial angle I am getting new Coordinates along the GC (around every 1 min of flight time) and then getting the Sunset and Sunrise times for each point as I go and seeing if I am in the night.

You can also perform the same analysis after the flight ends if you have an accurate track of the flight path from GPS data, which would tell you at any given time if the aircraft was flying in civil twilight time.


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How should I decide on the type of stringer to be used in an Aircraft's wing and fuselage?
I am trying to add stringers on the skins of an aircraft's wing as well as fuselage, for the same reason why they are present in most of the aircrafts i.e. to resist bending (and a possible buckling scenerio when subjected to aircraft loads during flights) by adding stiffness to the structure. However, I am not sure what type of stringer should be used since there exists alot of variations, and some of them are shown in the picture below.

Since there exists so many variations, it makes me believe that some specific benefits are associated with each of these variations, when subjected to a certain situations. So what things should I consider while making the optimum choice for the stringer shapes? In which cases will each stringer shape prove to be fruitful than rest of the stringers? How should I decide the locations of these stringers within the top and bottom skins of the aircraft's wing and fuselage?
P.S: I can conduct a FEA for the wing + various shapes of these stringers, but it will take too much time. I believe there exists a rule of thumb for the choice of each stringer shape depending on somethings.

At the conceptual level, the most significant issue is whether the stringer has to be resistant to buckling; will it be subject to significant compression loads, or will be almost exclusively under tension?  If compression loads aren't severe, the profile isn't that important and an L or T will work. If it has to take compression as well, you need the additional flange to stiffen the stringer against buckling without having to make the material thicker.
You will use the hat section when compression loads are really high.  Next down would be the I and J profile, then the C or Z section, then the T or L.  If the loads were pure tension, no stiffness at all is needed and a flat strip would do the job.
Access to fasteners and contact with adjacent objects also becomes an issue.  You might use a Z instead of C because you want easy access to buck rivets.  The C stringer will be harder to rivet.  On the other, hand, the flange of the Z channel may foul on adjacent structure and force you to use the C channel.

So you are saying that addition of an extra flange (although this extra flange is not connected to any skin as the already existing flange on a T or L section is rivete/glued to the wing/fuselage skin) will still be a better choice for a moderately high compression load? I mean I can increase the thickness of the already connected flange instead of inputting an extra flange on the bottom of the stringer (like in C or Z). So which one will be a better choice?

For compression load through the skin along the axis of the stringer, where the stinger itself has to resist bending or buckling when compressed along its axis. For a given bending/buckling resistance, it'll be lighter to use a C or Z instead of making the vertical part of a T thicker, because the C/Z  top flange adds the buckling resistance where it's most beneficial, along the top, whereas making it thicker, the extra material close to the base is not doing anything, just being ballast. Make a C section sample and and L or T sample from cardboard and see which is stiffer.  It'll be obvious.

I don't know why you said that the other option is instead to increase the thickness of the web (vertical part) of T beam. I was thinking that I should be increasing the height of it (not the thickness) since for the same increase in mass, the increase in height will result in more stiffer T beam overall.

I was assuming you had to select a cross section limited to the same dimension. But making it higher adds nowhere near the resistance to buckling as bending the same extra material over into a flange, so I don't know why you would do that.

Well, I checked out how would the moment of inertia change for a T beam when extra height is added to its web, as compare to adding extra thickness to its web (where material addition in both cases is the same). It turned out that adding extra height to the web of T beam would result in more moment of inertia hence making the stringer more stiff and more effective against the top wing skin / fuselage buckling.

Adding an extra flange to the stringer (like converting a T stringer to a I stringer or replacing T/L with a C/Z) will definitely prove to be a better choice, because, as you mentioned, C/Z would result in lighter weight overall than if I would be choosing to change the T/L stringer dimensions. But assume I don't have the availability of C/Z stringers, then modifying the T/L stringers' dimensions are the only remaining choice. And in this case, increasing the height of the web of T/L stringer will be a better choice than increasing the width of it, I guess.

Can I get a reply from you on the comments I made, John?

I think you've answered your own question.  Perhaps a tall and thick flange, lightened with lightening holes along the web to compensate for the thickness penalty.  Of course that would drive manufacturing costs up.


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Why do planes employ vortex generators if the laminar flows exhibit a far lower skin friction drag than turbulent flows?
I am a student and still relatively new regarding fluid flows. Our professor asked this and I can't find a source to answer this question.

Vortex generators are in most cases a late stage fix to get the flow conditions right in all corner cases. Maybe your professor should have asked about turbulators, because those can indeed hep to lower drag. Sometimes.

Laminar flows detach from the surface earlier than turbulent flow does, which means that with everything else constant, a laminar wing stalls at a lower angle of attack, and does so more suddenly and with less warning.

The unsteady nature of a turbulent boundary layer allows it to extract more energy from the freestream (flow which is not slowed down by the wing), thus the boundary layer stays energized and slows down later. This, as you have mentioned, increases drag, so there is a tradeoff between delaying stall and increasing drag.

You'll find VGs on the wings of trainer aircraft,so that they have forgiving stall characteristics...

...STOL/bush aircraft, for lower stall speeds...

and near control surfaces of all kinds of aircraft, to retain control when the control surface itself is in high angle of attack. This also increases their effectiveness so the designers can get away with making them smaller.

I wonder if it would make sense to build a plane with retractable vortex generators.

The effect of these devices is relatively minor, as mentioned in the answer below. The extra weight of a retraction mechanism will reduce or eliminate the slim benefits of VGs. Some WW2 fighters and the A-10 have auto-extending leading edge devices but they don't have the exact same working principle as VGs. Some claim that the leading edge devices on the A-10 serve to channel airflow to the engines in high AoA conditions.

The "horizontal tornado" created by the VG resides partially in and partially out of the turbulent boundary layer.  The effect is that the half-in-half-out circulation pulls freestream air down into the turbulent boundary layer, making it a relatively non-turbulent, although spiraling, flow.  It's a compromise; not as good as a straight laminar flow, but better than turbulent flow.
There is a drag reduction from the replacement of the turbulent flow with a non-turbulent-but-spiraling flow, but this can be offset by the energy consumed in creating the vortex, so it varies as to whether there is a net benefit or not, drag wise.
VGs are generally used for two purposes.  One is as a band-aid to improve a flow separation that is causing vibration or other control issues, often at high speed, usually ahead of control surfaces.  There may be a drag reduction that is more than the energy penalty of the VGs themselves, but often they are just to fix an issue like a dead area in an aileron's or rudder's range of movement near neutral, or delay turbulent separation at large surface angles, or to fix a vibration problem caused by turbulent flow.  On large aircraft you can generally assume there weren't there on the first prototype, and had to be added during development to fix a problem in a way that was cheaper than the alternatives.
The other is to delay flow separation near the leading edge of a lifting surface to a higher angle of attack. VGs on light aircraft mounted on wing leading edges are being used as a "poor man's slat"; they will provide about 1/3 to 1/2 the stalling AOA increase that a leading edge slat/slot does.  You put VGs on a Cessna 140, and the stalling AOA increases to somewhere around 18-20 degrees vs 15.  This is good for about a 4-5 mph reduction in stall speed.  VGs on the lower side of horizontal tails or on fins are for the same reason, to increase the surface's operating range.
It is generally found, on light aircraft at least, that the VGs' impact on cruise drag is a wash. You might think that an array of VGs on a light plane's leading edge would create quite a drag penalty at cruise speed, but the turbulence reduction even at cruise AOA is enough to cancel out some or most of the energy penalty of creating the vortices.  With most VG STOL kits there is only a minor, or often no, speed penalty when they are installed.

Just to be clear, at higher airspeeds / lower AoA, like on an airliner, VGs would increase overall drag, and that's why we don't see them on airliners except sometimes in front of control surfaces.  Because at low AoA, you can expect laminar flow over the whole wing.  Your answer implied this without stating it explicitly.

I don't think you have true laminar flow on any wing past the point of maximum thickness
even if it's a perfectly smooth one and most wings have some discontinuity that trips any laminar flow long before that (like a leading-edge-to-plank skin joint, or a retracted slat trailing edge). I think what we think of as laminar flow on a typical bumpy wing surface is really just a very thin turbulent boundary layer.  Where VGs appear ahead of a control surface it's because the boundary layer got too thick.  But to your point yes I expect they cause a net drag when used that way.


text:
Odd whining sound from planes passing over
I'm trying to figure out what is causing the sounds that I'm hearing from planes passing over my house. I'm located approximately 60 miles NW of ATL. The noise I hear sounds like a turbine rapidly spinning up, and then back down approximately 5 seconds after. My theory is that this is from an initial descent, relieving some resistance on the turbine blades, but can't quite find the sound anywhere else. I have never heard this sound prior to moving here to GA a year ago and I have lived near major airports near Newark, Virginia Beach, and several military bases throughout my career. I do not have a recording yet as the planes are not quite visible when this occurs and I also don't hear the approach.

Is the sound, or rather the pitch change categorically the same, or is there variation between each occurence?

See also: What makes the swooping noise when a jet flies overhead?

Is the rapid change in both pitch and loudness?

A recording would be helpful.

I believe what you are hearing is caused by the doppler effect.  https://www.physicsclassroom.com/class/waves/Lesson-3/The-Doppler-Effect

There doesn't happen to be a very large wall (such as a part of a large building, or a large free-standing wall) near you does there?  I heard some strange sound effects a few days ago as GA aircraft took off and landed on a nearby runway, that were clearly due to the way the sound was bouncing off the long metal hangar wall located right next to the place where I was sitting.


text:
Looking for techniques to model resistance to roll rotation in a very simple, force-based flight model
I'm new to flight dynamics programming and am curious to know how people model an aircraft's resistance to rolling in very simple force-based flight models (not CFD, etc.).  For example, after a full deflection of the ailerons, the stick is returned to center and the aircraft will stop rolling.
I assume I should be looking at factors including dynamic pressure, wing area, and a center of pressure for the wing.  I'm just not sure if I should just be modeling the "wing pushing against the air that it is rolling into" or if there are other more significant physical principles at play.
Essentially I am trying to create a model in which I can tune maximum roll rates against an aircraft's tendency to want to stop rolling.
Thanks, and sorry in advance if this is too vague, but any info will certainly be appreciated and will help steer me.

Please read this answer and combine it with this answer.

Thank you!  (I needed better search terms ;-) )

The way this is commonly done in simulators is using linearized stability derivatives. For your example, one could calculate the rolling moment on the aircraft as the sum of such terms as:  rolling moment due to aileron deflection angle, rolling moment due to roll rate (roll damping), roll moment due to side slip angle, roll moment due to yaw rate, roll moment due to rudder.  For doing simulation each of these coefficients can be precalculated based on flight testing or CFD and then during simulation lookup tables can be used to find the current value.
My suggestion is that you take a look at JSBSim which is a cross platform opensource flight dynamics model that is used by FlightGear for example.  JSBSim allows one to build an aircraft model by defining the values in an XML file.  The website includes documentation, some links to papers and books, and example aircraft that are very useful.

Thanks!  That's the basic approach I take, although a bit simplified as this is for a mobile game.  Basically, I'm adding new terms to the model as it gets more sophisticated.  I don't need precision, I just need it to "feel good" and allow me to differentiate between aircraft.
I've looked at JSBSim and LarcSim in the past as references, but it takes me a while to digest the math ;-)

This is far from a complete answer, but I want to point out that you need to recognize that the motion of any given part (e.g. molecule) of the aircraft through the airmass creates an apparent wind or "relative wind" in the opposite direction.  If an aircraft is changing bank angle (rolling), the "relative wind" actually becomes "twisted" into a corkscrew-like shape.  For example, the wingtip that is rising will feel a downward component in the relative wind, while the wingtip that is descending will feel an upward component in the relative wind.
This link should be of some interest -- note that the green arrows labelled "motion" are not both pointing in the same direction, and thus the direction of the local relative wind (which is opposite to the direction of the "motion" arrows) is not the same at each wingtip, and thus the angle-of-attack of each wing cannot be the same.  The angle-of-attack of the rising wing has been decreased (or in extreme cases, has actually become negative), and the angle-of-attack of the descending wing has been increased.  This creates the "roll damping" phenomenon-- a roll torque acting to slow the roll rate-- which can be loosely described as an inherent aerodynamic "resistance" to rolling.  This phenomenon is central to the dynamics that you are trying to model.
From the phrasing of the question, it seems that you already understand much of this, but I just thought that this answer might put it into a slightly different perspective that might be helpful.
PS the link noted above leads to a discussion of yaw dynamics (adverse yaw), but that's not really what I'm trying to focus on here.  I'm just using it as a useful illustration of the "twist" in the relative wind due to rolling, and the resulting "roll damping" or "resistance" to rolling, regardless of whether "adverse yaw" is also entering the picture in a significant way or not.


text:
How to decide the diameter of a propeller and number of propellers needed in a UAV I am designing?
I want to design a turboprop aircraft. I know all the design parameters such as lift, thrust, weight etc at a given flight stage. I want to know what the size of the propeller should be.

There is an analytical process for selecting a propeller, but in the most straightforward cases it begins first with the selection of the engine. The propeller choice then can be made almost immediately.
Since you state that the plane will be driven by a turboprop, you have greatly narrowed down the propeller possibilities, and once you have selected a horsepower requirement for your turboprop engine, you have automatically narrowed down the propeller choice even further. Then, once you have selected a particular turboprop engine from a specific manufacturer, your propeller choices are narrowed down to just a couple of possibilities.
Just about the only design choice remaining after you select, for example, a PT-6 with a certain shaft horsepower output specification, will be the prop diameter needed to achieve the correct ground clearance for the engine installation, which may (for example) dictate four blades to absorb the engine power for a small diameter blade disc rather than three blades for a larger diameter disc.
Note also that no prop manufacturer is going to design for you a custom prop from scratch unless you can guarantee the purchase of tens of thousands of propellers of that custom design, and the design process will require years to go from an empty CAD file to a certificated prop being bolted onto an engine.
From an engineering practicality standpoint, your best bet would be to select the engine and then choose the most commonly-used prop in current manufacture with the longest production run and the greatest number of units in the installed base.


text:
Is the Mach number shown by an Air Data Computer considered a "true" Mach number?
I am trying to find more information on "true" vs. "indicated" Mach number (not airspeed). I've found older fighter aircraft manuals online that have a conversion chart from one to the other, but the modern jets I've flown don't have such charts.
During a recent flight at 41000 feet, at a Mach number of 0.81, a true airspeed of 476 knots was displayed on the EFIS. In the standard atmosphere, 81% of the speed of sound is 464 knots at that altitude. Sure enough, the actual temperature was some 13 degrees C warmer than the "standard" -56.5 C, hence the true airspeed of 476 knots instead of 464.
But that leads me to believe that the Mach number I am flying is not really "true".
The relevant flight manuals do not use the words "indicated" or "true" to qualify the Mach number.

For subsonic aircraft the Mach number is normally measured from dynamic pressure and static pressure, very similar to the way calibrated airspeed is measured.
$$M_a=\sqrt{\frac{2}{\gamma-1}\left[\left(\frac{q_c}{p}+1\right)^\frac{\gamma-1}{\gamma}-1\right]} $$
with:

$M_a$, the Mach number
$q_c$, the dynamic pressure
$p$, the static pressure
$\gamma$,  the ratio of specific heats (1.4)

If there is an error in the measurement of either the dynamic or the static pressure both the indicated airspeed and Mach number will be affected.
Note that the Mach number has no direct dependency on temperature.
The true airspeed is calculated by the ADC from the Mach number and the outside air temperature.
$$V_{TAS} = M_a \cdot \sqrt{\gamma R T_S}$$
with

$R$, the specific gas constant (287.05 for dry air)
$T_S$, the static air temperature

The indicated true airspeed has a direct dependency on the static air temperature ($T_S$,SAT) also known as the outside air temperature (OAT). The static temperature cannot be measured directly since the air will heat up on impact with the temperature sensor due to adiabatic compression. Instead the total air temperature ($T_\mathrm{total}$, TAT) will be measured.
The relation between the measured total air temperature and the static temperature is given by:
$$\frac{T_\mathrm{total}}{T_{s}}={1+\frac{\gamma -1}{2}M_a^2}$$
Since the measurement probe may not recover all the energy from the adiabatic heating a correction factor is introduced:
$$\frac{T_\mathrm{total}}{T_{s}}={1+\frac{\gamma -1}{2}eM_a^2}$$
This 'recovery factor' $e$ is determined empirically for the temperature sensor used.
The display on the EFIS will show the OAT, which may be slightly off if $e$ is not entirely correct. This will also affect the "true" airspeed indication.
To conclude; anything indicated in the cockpit can contain measurement errors, regardless whether it is called 'indicated' or 'true'.
With the introduction of digital flight data systems the error correction tables have been moved from the manuals to the computer, which automatically corrects for them.

With all that MathJax, I thought this was a Peter Kämpf answer, and I mean that as high praise!

The point is that there is indicated speed and true speed and they represent different physical quantities (dynamic pressure and speed), but there is no such pair for Mach number.

I was chasing this because the North Atlantic procedures manual specifies that when assigned a Mach number to fly, this should be the "true Mach number". The emphasis made me curious.

@Ugo the North Atlantic Operations & Airspace Manual does indeed distinguish between indicated and true Mach number. It says: For many aircraft types the cockpit instrument displays the True Mach being flown. However, for some types the AFM notes a correction that must be made to the Indicated Mach to provide the True Mach. I don't know your aircraft type, but if there is nothing in the AFM then you can assume the Mach number displayed is the True Mach number. In that case the air data computer will apply the corrections before data is send to the display.

@FreeMan Thanks, I take that as a compliment! I am not exactly shy of using MathJax either, this site was two days into private beta when I first needed it  :-)

Mach is a number in relation to the speed of sound. The speed of sound is solely dependent on the outside air temperature. Hence unlike airspeed there is no such thing as 'indicated' mach.
$$ M=\frac{TAS}{a}$$
$$ a= \sqrt{1.4*288.15*T}$$
Where $a$ is the speed in m/s of sound and $T$ is the temperature in Kelvin.
The old jets needed conversion charts since the true airspeed was not computed by computer and machmeters used a best estimate value limited by the error in pressure. The following is from a USAF handbook on how the Machmeter works:

This document by Airbus also suggests you are looking the ratio of True Airspeed.

The eyes of all fighter pilots I've met would glaze over looking at that.  They just want to look at a gauge or readout :)

Indicated Mach is what your Mach indicator reads during flight.  True Mach is basically indicated Mach that has been corrected for pitot-static system position error and instrument error. (Same as the difference between indicated airspeed and calibrated airspeed).
Position error is caused by the location of the pitot tubes and static ports on the aircraft. This is due to the shape of the aircraft and the way the air flows around it. Engineers try to locate them in areas where the error is at a minimum, but there's always some error. The amount of this error is determined during flight testing and charted in the flight manuals. Some more modern aircraft have software that will automatically compute their calibrated airspeed and true Mach number. Most aircraft, however, still use indicated airspeed and Mach number.
Instrument error is the difference between a calibrated input to the Mach indicator and the actual reading it gives. The Mach indicators I've worked with usually have a tolerance of +/- 0.03 Mach. So, for example, if a technician inputs a calibrated value of 0.70 Mach and the indicator reads 0.72, it's within limits.
Temperature has nothing to do with the way Mach number is calculated in aircraft flight instruments; however, temperature does affect true airspeed.
In your example, 41,000 feet, Mach 0.81 and temperature 13 degrees above standard (that means -43.5 degrees C static air temperature), I calculate the true airspeed to 478 knots. Your total air temperature was probably reading about -13 degrees C, right?

Thx for the clarification. Since it has been a while, I'm afraid I can't say anymore what the TAT was.

Equivalent airspeed is not speed at all. It is dynamic pressure, indicated as speed at which that dynamic pressure would occur at sea-level standard conditions. And indicated airspeed is equivalent airspeed plus measurement errors (calibrated airspeed is cleared of those errors, that can be effectively estimated).
So there is an indicated/equivalent airspeed and there is true airspeed and they are different physical quantities.
There is no quantity that would be expressed as Mach number, but would actually have different physical significance. So “Mach number” only has one meaning. How it is measured and what are the errors is already well covered by the other answers.

It is not correct that on most aircraft including the newest Boeing, Dassault, bombardier products only display indicated Mach. You do need to check your manuals.  Only the Gulfsteam aircraft display true Mach.

Welcome to Aviation.se!  Can you provide a link to support your statement?

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/3.0/


text:
How does one calculate the Mean Geometric Chord in extended Trapezoid Wing?
The general formula to calulate MGC of a wing is given for a trapezoid in many books but there isn't an example showing how to calculate it for a wing shaped like the one below. I tried to solve individually for section 1 and section 2 and take the mean between those values but couldnt get the solution. I just want to derive a simple formula in case the wing looks like this.

For the mean geometric chord, calculate wing area divided by span.
For the mean aerodynamic chord you integrate chord squared over span and divide the result by wing area.
$$l_\mu = \frac{\int^{+\frac{b}{2}}_{-\frac{b}{2}}l^2dy}{S}$$

So, what would be the $l^2$ for both of them combined be here?

@SherlockHomies l is the local chord. l² is local chord squared.


text:
Below what altitudes do shock waves form?
For a shock wave to form, the air must have a certain density. Surely in Thermosphere or even upper parts of Mesospheres the air is very thin. I was wondering if there is a formula related to the Mach Number and the probability of shock wave.

Your question does not make sense. There is no "probability of shock wave". You are either supersonic and get a shock, or not. The solar wind is supersonic w.r.t. the interstellar medium and it produces a shock (termination shock) in space (where the air is very thin).

@Bianfable: Yes, if you want to get tecnical, quite a ways beyond the orbit of Pluto :-)

Shock waves form any time the speed of the airflow over or around a vehicle exceeds the speed of sound.
The local speed of sound varies with ambient temperature in a well-defined way; in general it goes down slightly as you climb higher.

Every reference I've seen talking about mach # says it's purely a function of temperature and I've always wondered if and to what extent pressure comes into it.

changing the temperature will change the air density, which will change the speed of sound.

Yes but when you refer to "ambient pressure" it tends to infer altitude or barometric pressure.  That needs to be clarified.  If you said "temperature/density" that would be more accurate perhaps.

@JohnK The speed of sound in an ideal gas is proportional to the square-root of the temperature, but not the pressure. Both temperature and pressure affect density, but only temperature affects speed of sound. Of course, at some point it does not make sense any more to model air as an ideal gas and this will no longer work, but for the altitudes aircraft typically fly at, it works quite well.

@Bianfable That has been my understanding of it.  So to my point, should the post be corrected to remove the mention of "ambient pressure"?  Someone reading that could infer the speed of sound is affected by altitude changes that are to one degree or another independent of temperature.

@JohnK I agree, the "ambient pressure" should be removed.

@JohnK how about now


text:
How do i find a supercritical airfoil for my preliminary design?
The following information is available but i don't exactly know where to get the information about SC Airfoils from. Do Airbus , Boeing use secret airfoil that they don't disclose?
Cruise Speed = 240 m/s or 0.7 Ma; Chord length = 5.5 meters
Using online tool to get the Reynolds number gives a very high number of about 85 million. Using the standard setting for kinematic viscosity of $1.4207E-5$.
1.How do I find a SC airfoil for a transport jet of about 150 Pa @ 0.7 Ma?
2.Why are my Reynold's number so high? It should be around 25-30 Million.

Answer to the implicit question: Yes, the more recent airliner airfoils are indeed secret. Look for reports like this to see what is out there.
Answer to question 1: Try the linked NASA Technical Paper 2969.
Answer to question 2: Your viscosity is for sea level. Try to use the value for the tropopause and it will be only ⅓ as large.

Thank you but the link on NASA Technical Paper 2969 is broken. (Both links don't work)
Also, that means regional aircraft that don't fly very high have very high Reynold's numbers, which implies they suffer more drag right?

@SherlockHomies Thank you for letting me know. Now I have changed the link to something hopefully more permanent.


text:
Can an aircraft have a lifting fuselage that only generates lift at certain speeds?
I came across the blended wing body designs and their advantages etc. They are still very far from reality and require 20 more years till we see them fly. Isn't a conventional fuselage design with a somewhat flattened shape that generates lift during cruise only, a better alternative for now. Would it be possible? If yes, then that means the fuselage usually stalls in all other configurations but during a cruise at a particular AOA. That does mean that drag increases during climb and decent but the efficiency gained during cruise should mean that it is beneficial for a long-range flight?

I don't think you need the "only certain speeds" part. At least, not in the title

I think you are looking at this backwards...  (at least for a utilitarian passenger type aircraft)
First, such a design is most certainly possible, but it would create more problems than it would solve.  Wings don't need extra help producing lift at cruise speeds, that is when they are most efficient.  Instead, wings can use a little extra help at slower speeds, which is why they are typically equipped with lift enhancing features like flaps and slats.
Second, producing lift creates induced drag.  You want the fuselage to be as streamlined as possible to produce the least amount of drag at higher cruise speeds, not more.  And if your lifting fuselage is fully stalled at all other phases of flight it will be producing MASSIVE amounts of drag.
This full-stall drag penalty would create significant performance problems in all other phases of flight that would likely cancel out any small efficiencies at cruise speed, such as redesigned wings, more powerful engines, etc.  I don't see anything to be gained by such an idea.
And finally, what makes you say that we are 20 years away from a blended wing body design being able to fly?  There have been all kinds of designs built and flown in the last century, I don't think there are any technological hurdles to this type of aircraft.

As in terms of passenger seating and evacuation etc BWB has problems I meant. Also thank you for your answer exactly what I was looking for.

to my knowledge there are flight stability requirements for civil aircraft which are not there or as restrictive for military aircraft. Hence things like aerodynamically unstable airframes that get stabilized via control systems wouldn't get certified for civil aviation (airliners, general aviation etc), even though there are planes like the B2. I'm not sure though if you could meet areodynamic stability requirements using a flying wing / blended body..

for evacuation i don't see the big problem .. if anything, the passengers are thinner distributed over the aircraft, I guess it's just something to design for.

Why adjust for lift only in cruise? Why not benefit throughout the flight envelope?
One aircraft that had a wide, lifting fuselage was the Lockheed SR-71 Blackbird. The fuselage was widened with sharp "chines" (a term taken from boatbuilding) extending forward from the tailless delta wing. During takeoff and landing the chines acted as vortex generators to provide vortex lift over the wing, similar to Concorde. During supersonic cruise the chines acted as fore wings to provide extra lift, stabilise the aircraft and stop the centre of lift moving back, as usually happens. But at high subsonic speeds the chines contributed little aerodynamically.
Some hybrid airships, such as the Airlander 10 have widened hulls to contribute lift, which of course only works as the ship picks up speed. But as far as I know, nobody has produced accurate numbers on the effect this has on cruise efficiency.
As another answer points out, a wide fuselage is structurally inefficient and tends to add weight. For large types such as the Boeing 747 and Airbus A380, designers found that they actually saved more weight, and thus improved overall efficiency, drag and fuel consumption the most, by stretching the fuselage upwards and adding a second passenger deck.

It would be better to sat "a shallow fuselage"

The problem with squashed fuselages is that they threaten a weight increase for little benefit. The fuselage, with its inherently small span, can generate little extra lift compared to the wings. The cost is that by reducing the depth of the very large beam that is the fuselage, you are exponentially increasing the amount of material needed to absorb the bending moment of the nose and tail.

In principle: yes, or well "mostly".
Though first lets tackle the elephant in the room: it's not the surface itself that generates lift - it is the geometry. And the obvious solution hence would be to deform the fuselage at higher speeds so it can create lift.
What you would do is have a fuselage that is "just stalling" when flying normally. This means air separation is just about happening in "slow" conditions. This means the airflow around the fuselage has just a little too little energy to stay attached to the surface.
If we then fly at a higher velocity the airflow around the fuselage has more energy. With the little increase of energye the flow could stay attached to the surface.
Now this is only a principle: since there is also the problem that lifting surfaces have huge hysteresis when going into the stall region and recovering. So the airflow would never reattach itself to the surface. You would have to add some active guidance to first attach the flow to the surface again.. - Or instantly being at large speed and never going slow in the first place.


text:
Is there a better solution than the U-shaped tailplane for this Airbus concept?

Image source: airbus.com
This U-Shaped tail is from a concept aircraft from Airbus, I was wondering if there is an alternative but just as good solution to the U-shaped tail. Using a canard in the front for pitch and winglets on the wingtips?

Could you clarify what ‘good’ means in this context, and whether/why you consider the illustrated design to be bad?

Good as in less surface area of the tail.

Off-topic: This appears to me to be another double-decker super heavy along the A380 lines. Hasn't Airbus killed the A380 because there's zero demand for it? Haven't they learned any lessons from that fiasco?

In airplane empennage design, there is a thing called Tail Volume Coefficient. Mind you, there are no volumes here, but you are working with $m^3/m^3$. It is calculated as follows:
Horizontal tail volume:
$V_{HT} = \cfrac{ l_{HT} \cdot S_{HT} }{ c_{REF} \cdot S_{REF} }$
Vertical tail volume:
$V_{VT} = \cfrac{ l_{VT} \cdot S_{VT} }{ b_{REF} \cdot S_{REF} }$
here

$c_{REF}$ - mean geometric chord (~MAC)
$b_{REF}$ - wingspan
$S_{REF}$ - reference wing area
$l_{HT}$ - horizontal tail arm
$l_{VT}$ - vertical tail arm
$S_{HT}$ - horizontal tail area
$S_{VT}$ - vertical tail area

Now, with that in mind, you can have a perfectly reasonable cruciform solution, U-tail, H-tail, or triple-tail solution, or whichever.
However, freely choosing empennage configuration is not the only condition in design. Engineers likely have other requirements. These two vertical stabilizers (VS) look relatively slender. Perhaps a single VS would be too slender and cause structural issues, perhaps flight dynamics department required better yaw or sideslip control, in which two VSs would maybe be proved better. I think Russians designed An-225 with an H-tail to carry extreme payloads (like Buran), whereas Americans didn't modify 747's empennage for Space Shuttle carrying. There are a number of considerations here. One of which, mind you, is also aesthetics, especially for a passenger airliner.
So, is there a better solution than the U-shaped tailplane for this Airbus concept? It depends. There is no single universally best solution in these things.

Equations from S. Gudmundsson: General Aviation Aircraft Design

Americans did modify the empennage of Shuttle Carrier aircraft—it has additional vertical stabilizers attached to the ends of the horizontal stabilizer. The dorsal load reduces effectiveness of the central vertical stabilizer, so they had to add a bit of H configuration too.

@JanHudec You are right! I completely missed that!


text:
Why do some military aircraft carry two datalink pods?
I was taking a look at pictures of the SLAM-ER when I noticed an F/A-18C carrying two AWW-13 datalink pods on its left wing. Why carry a second one? Does it increase signal strength or something?

Source: https://commons.wikimedia.org/wiki/File:F-18C_with_SLAM-ER_missile_and_AWW-13_pods_in_flight.jpg

This being a question about military aircraft and intel systems, you are unlikely to get accurate factual answers.  As pure speculation though:  reasons may include  Redundancy; extending bandwidth and/or channel count;  Testing, calibration, simulation; training etc.

Btw, all in all a very peculiar payload on this one...

That pic is from "the Naval Air Warfare Center, Weapons Division (NAWCWD)"
So, testing and development.
Possible reasons (purely speculative):

Testing capability/performance from the 2 different wing stations.
Test/compare different software configs in each.
Ferry one to somewhere else.


text:
How did they solve the compressor stall issue of the F-14A in the B?
I know that the F-14A was notorious for having compressor stalls during high AOA or with quick thrust changes, and most of the issues were solved in the B. Externally there doesn't seem to be much difference in the intake, so how did they solve it?

The F-14A and B have different engines.

@efe Thanks, I know but specifically what made them not suffer from the same issue?

Grumman changed the F-14 powerplant from the Pratt and Whitney TF-30 engine to the General Electric F-110 engine when the F-14B was developed.  This not only provided the airframe with an extra 16,000 lbs of thrust compared with the old TF-30 engines but also a much more stable, reliable gas core as compared with the P&W design.  I don’t know if they have managed to wring out the issues in the F119 and F135 engines, but Pratt and Whitney engines have been notoriously finicky and prone to compressor stalls if not petted nicely.  GE engines, particularly military aircraft engines, are some of the most robust and reliable jet engines out there.


text:
can someone describe difference between U2 spyplane (glider-like) WING and F-16 Delta Wing
I'm trying to learn induce drag and parasite drag and LIFT and load factor for glider. if f16 is loaded with fuel is it difficult to control at slow speed. we know rectangular wing is best slow speed wing. and i know the delta wing is for fast speed and a glider never needs that much speed.
a fully loaded f16 would have very high amount of parasite drag ? how much induced drag when it flies, compared to tapered wing ?

There's far too much here for one question.

i only wanted a simple basic answer about drag. the u2 rectangular/tapered wing could stay aloft without an engine; but delta wing requires massive amounts of power and has very small aspect ratio. i wanted just a few comments about  their drag amounts to understand the two types of drag.

This is a horribly complex business which I will try to horribly simplify for you.
The biggest difference between these two planes is one is subsonic and the other can be either sub- or supersonic. That means that the design principles for them are completely different, and once optimized, their wing designs come out being totally different.
This makes it practically impossible to make valid performance comparisons between these two classes of designs.


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Holding *west* on the 090 radial?
This question was on a practice instrument test:

You receive this ATC clearance: "HOLD WEST OF THE ONE FIVE DME FIX ON THE ZERO NINE ZERO RADIAL OF ABC VORTAC, FIVE MILE LEGS, LEFT TURNS…" You arrive at the 15 DME fix on a heading of 350°. Which holding pattern correctly complies with these instructions, and what is the recommended entry procedure?

With this image:

I've only flown in practice holds where holding west was on the 270 radial, and holding east was on the 090 radial. I get that in this example, I'm holding west of the 15 DME, but I didn't know ATC would assign a hold like that. Is this a real situation, or is this a bad practice question?

The #2 is bogus, but in a way unrelated to the fix definition: you always cross the holding fix while on the defining radial, and then turn outbound in the specified direction. That's #1. With a map display you probably could fly that pattern 2, but not with more basic instrumentation, which is what the holding rules are written for.  For #2 illustration to work, the triangle for the fix would have to be moved left, roughly under the "15" notation. (And then you'd be holding east of the fix.)

Let's break this down to its parts.

HOLD WEST OF THE ONE FIVE DME FIX

Yes, this is why the depicted holds are west of the fix, not west of the VOR.

ON THE ZERO NINE ZERO RADIAL OF ABC VORTAC

This gives us the holding course.  Don't get confused by radials/inbound/outbound terminology.  Because the hold is west of the fix, the inbound course to the fix is 090.

FIVE MILE LEGS, LEFT TURNS…"

This is a nonstandard pattern.

You arrive at the 15 DME fix on a heading of 350°.

This implies one of two things.  Either the 15 DME fix coincides with a 2nd VOR radial that was assigned as a course to the intersection, or an RNAV direct course to the fix was assigned.

Which holding pattern correctly complies with these instructions?

Because of the nonstandard left turns, pattern #1 is correct.

What is the recommended entry procedure?

Direct entry is recommended.  This can be the most confusing part.  Arriving from the "right" side of the "left" holding pattern on a heading more than 70 degrees from the outbound course (80 degrees in this case), it should be a direct entry.
Using what I call the "pen trick", hold a pen vertically over the heading indicator, rotate it 70 degrees to the left (for a left hold) and then check the sector of the outbound course 270.  This course falls below the pen, which is the direct entry sector.

Is this a real situation?

Yes.  Think of it as a 270 radial from the holding fix.  In this case, the holding fix is not a VOR.

As a Center controller, if I'd issued this clearance, I'd expect you to fly to the fix, then start your left turn into the five mile leg. It's unusual, as I would probably send you to the VOR first, to set you up on that 090 radial, or have you join the radial at some point before the fix.
As far as item 2 goes,the holding fix should always be on the leading end of the pattern, in other words, hit the fix, start the turn, so item 2 is not valid. That's a "hold east" pattern with left turns, and it's on the wrong side of the fix.

The fix that you are using for the hold is on the 090 radial, at DME 15. You are holding east of the VORTAC, but west of the fix. Assuming you have adequate equipment to identify the fix, this is a perfectly valid clearance- there's not always going to be a VOR right where ATC would like you to hold!
Holds like this are exactly why they need to give you a direction from the fix to hold from to begin with. If you are told to hold at the VORTAC on the 090 radial, you already know that you'll be holding east from the VORTAC without being told. If you were just told to hold at the 15 DME fix on the 090 radial without a direction, that could be two different holds: should you hold east of the fix (from DME 15 to 20) or west of the fix (from DME 10 to 15)?
If you don't have a DME or a suitable RNAV replacement you cannot identify the fix and you should refuse the clearance if it is mistakenly given.

@MichaelHall The example 2 is nonsense; see my comment above.  I think this answer does address the underlying concept that drives the question.

@MichaelHall As I read it, OP's question is "Is this a real situation, or is this a bad practice question?" OP doesn't ask which of the two is correct.

@MichaelHall "This is a perfectly valid clearance" is meant to be an answer to that.


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Why don't flights fly towards their landing approach path sooner?

For example shown here, the flight is heading to the centre of the airport, until it gets close when it then moves into it's landing path. This is an inefficient use of time, fuel and emmissions, why can't the airport tell the aeroplane exactly which runway and direction it will land earlier so it can more efficiently head towards the approach.

Sequencing... There is more than one plane trying to land or take off...

Why can't they still sequence with a wider area? To maintain separation they could tell a plane to slow down so that when it reaches the straight runway approach it's correctly spaced between other flights (sorry errors in my terminology).

With a wider area when controllers have to make changes the corrections required by the planes may be much larger. Suppose for example in your diagram that ANZ1115 has to be diverted to a runway with an easterly approach when it's already far to the south lined up with the runway it was originally assigned. That's going to be a big circular path.

One of the posters here is a controller @expeditedescent I  believe, who would be the best person to answer.

Related https://aviation.stackexchange.com/questions/43160/how-frequent-are-unpublished-holding-patterns-outside-general-aviation/43169#43169

From the approach direction, the flight was presumably from New Zealand to Sydney which is about 2000 km. How much "inefficiency" does this landing approach add to the total flight? I would guess less than 1%.

@alephzero exactly, it's extremely common to have things look inefficient at the micro level but it actually maximizes the macro level efficiency.  It's like squabbling over pennies on a deal worth millions.

could you be wildly overestimating the efficiency "problem", @AndrewHarvey ?  that plane just flew from LAX !  tiny wind/etc variations over flights (even "short" flights) completely swamp what you mention here.

Last-minute turns onto the approach path are much more common on short-hop flights to small airports. Ryanair is notorious for "handbrake turn" approaches: that said, because their pilots do several landings a day like this, they have much more hands-on flight experience than a typical long-haul pilot.

Okay so the savings with a more direct approach aren't large enough to make it worthwhile implementing a more efficient solution, and perhaps also ATC aren't incentivised to change.

Huh, ANZ. I could've sworn Air NZ flights had flight numbers beginning with just "NZ"

In general, IFR flights through controlled airspace use airways (highways in the sky) to fly between waypoints. The particular flight you show looks like it arrived via the N774 airway to a waypoint MARLN:

(skyvector.com)
The traffic flow around busy airports like Kingsford Smith (YSSY) in Sydney is usually structured using Standard Instrument Departures (SIDs) and Standard Terminal Arrival Routes (STARs). Your example was probably on the MARLN5 RNAV STAR:

(from the Jeppesen chart for MARLN5 at YSSY)
From somewhere after the JAKLN waypoint, the air traffic controller (ATC) would have instructed the flight to turn right to intercept their final approach path (probably to runway 34R).
All of this structure (airways and procedures around busy airports) exists to allow for an efficient flow of traffic that can be easily managed by ATC. There are many things to consider when these paths are designed:

avoiding conflicts between aircraft (e.g. between departing and arriving aircraft or between flights from different airports in the area)
restricted airspace (e.g. airspace reserved for the military or avoiding flights near sensitive areas, like nuclear power plants)
noise abatement (especially near large cities you want to avoid overflying the city center at low altitudes)
terrain (not really relevant for Sydney)

Nonetheless, one can deviate from these fixed routes. ATC might clear an aircraft on a more direct route if traffic and restricted airspace allows this (very common right now due to the pandemic). Some countries have even removed all high altitude airways and replaced it with Free Route Airspace.
The problem with setting an aircraft on a direct route for final approach interception is that this would have to be done far away from the airport. The aircraft needs time to descend and slow down (usually more than 100 NM). At this point they are typically not handled by the approach controller for the airport they are landing at, but still by the Area Control Center (ACC). This would require significantly more coordination between various controllers and is probably not very efficient in busy airspace. During the current pandemic with significantly less traffic, you might see it though.

Thanks for your answer. From your chart, if when at Marlin the flight would be told the final approach, it could then start turning to go direct towards Jakln and onto the landing approach. It sounds like Free Route Airspace aims to do something like this (but maybe not yet this close to the airport). So it sounds like it's just down to more coordination between the approach controller and the ACC, and potentially more computer automation to determine the most efficient route while still working within constraints (terrain, noise, distancing between aircraft, go rounds etc).

When ATC tells you "cleared direct to JAKLN" when you are at MARLN, then you suddenly have to descend faster. Airliners already fly an idle descent path (meaning engines are at idle), so descending faster is only possible with speedbrakes. That may save some time, but not really much fuel. That requires knowing about the shortcut much earlier and therefore starting the descent earlier.

I see, though to me that just says ATC need to communicate this earlier so the aircraft can descend earlier.

Exactly, they need more communication and coordination between different controllers. We definitely see a move towards this (like Free Route Airspace for high altitudes), which  is probably supported by newer technology and clever computer algorithms. Since you make a valid point (saving fuel is always a good thing), I guess we will see more direct routing in the future, but sometimes aviation is slow to move on...

Another factor might be wind direction (and hence landing direction).  Don't know about Sidney, but around here it's not uncommon for wind direction to change during the day.  If your flight is aiming for an approach from the south, and the wind shifts to favor an approach from the north, you've wasted even more time.

Side note, what are these waypoints? If they were on land I'd guess they were radio beacons. But these are over the water. I'm assuming there are not floating beacons. Are they defined as intersections of lines defined by other beacons, or GPS coordinates, or what?

@user253751 Some waypoints over land are radio stations (like VORs or NDBs), but most of them are just defined by their coordinates today. The STAR is marked as an RNAV STAR, which stands for Area Navigation. It requires an aircraft to be able to fly between arbitrary waypoints (e.g. using GPS).

Most airports have approaches designed to be as straight-in as possible for the reasons you describe. Cases like this one in Sydney are in the minority (for major airports at least).
This is the approach route in question:

As to why YSSY specifically has such an inefficient approach? I'm not 100% certain but I can think of a few contributing factors. Sydney airspace overall is a mess, with two defence force zones, large GA airports, and restricted airspace over the harbour. Also, due to the proximity of the airport to the city millions of people are affected by aircraft noise. There are powerful lobby groups, and enough electoral seats under the flightpath that the federal government could easily fall if they took a pro-airport stance such as lifting the curfew or the hourly movement cap. Changes to any of the flight paths, even just over the ocean, require community consultation and could stir up a lot of angst. Basically, it's a huge job.
All of this leads to: the flight paths haven't had a major update in a long long time. I suspect that this route merely replicates what the route was before we received the flexibility of GPS/RNAV approaches, back when you basically flew VOR to VOR. Nowadays, you would only design the approach in this way if there was some other airspace restriction or terrain (but being over the ocean, neither of those apply).
Fortunately, with the new Western Sydney airport finally due to open in 2026, a whole re-think of the airspace is about to commence and the approaches will hopefully be made a tad more efficient.

I don't agree with your first paragraph. Many large airport, at least in Europe, have RNAV STARs similar to Sydney where all traffic is directed toward a downwind leg before joining final

Thanks, that makes sense, basically too many stakeholder issues to change flight paths, so instead they leave them in a few set paths. It's funny that it affects paths over the ocean too though. End of the day the current inefficiency gives me more time looking out the aircraft window observing the city so not complaining, but had been wondering why for a while.

When the landing approaches, pilot has to reduce the speed of the aircraft and maintain the lower speed and distance to avoid accident. Pilot has to slowdown or else he will not be able to land at the destination airport. Moreover due to the congestion in the aircorridor, pilot can be asked by ATC to take more rounds so that the landing is safe and enough time is provided for other aircrafts that are either landing or taking off or taxiing. Once I saw One International airline, suddenly abort landing and raise the altitude, may be due to ATC's instructions. I can only see the flight above as the engine made a roaring sound all of a sudden.

ATC isn't incentivized to reduce CO2 emissions. To do so would require re-architectiing their whole SIDs and STARs (to make them dynamic based on AC type, weather, traffic, and other factors). I vaguely recall reading about a (US) FAA initiative to modernize the vector airways to optimize for descent rates, etc but that will take years. Ultimately, it's the airline who bears responsibility to minimize fuel consumption and government who is responsible for separation.
I'm not myself an aviator, but I imagine that the downwind, crosswind leg, and final also give the crew a good feel of the surface meteorological conditions.
My final $0.02: ultimately the best way to minimize CO2 is to not fly for leisure. Look at youtube for all the frivolous flights of people globe trotting just because they can. It's simply un-sustainable.

Strongly disagree ... the purpose of ATC is "preventing collisions and expediting and maintaining an orderly flow of air traffic." Of course safety is #1, but it is very closely followed by efficiency.

@expeditedescent, he emphasized that ATC is NOT incentivized to reduce CO2.  So what are you disagreeing with?

ATC is not incentivized to keep an airplane in the air longer that it needs to, its role is also to manage traffic and thus a "useless" flying aircraft is a burden for them. On top of that this is not true that there are no optimization of routes. STAR approaches are one and there are larger scale ones https://www.eurocontrol.int/concept/free-route-airspace

@brice we have different versions of "optimize". as OP pointed out, the crook-shaped approach in the photo is an utter waste. if the goal is to maintain sep, there is a way to do that while also giving the AC an optimal glide path (if there were no ATC rules, just solving a multivariate optimization math problem), which would require slowing them down during cruise to allow each AC a perfectly optimal and separated glide into final. ATC doesn't care about saving the airlines money. What's left is semantic arguments about what is "optimal".

From a purely theoretical standpoint I'm sure you could, as you say, just solve it as a "multivariate optimization math problem". However, this is the real world. You have to add a bunch of variables and random noise to your data, and also realise that the sensor input you receive is not necessarily 100% accurate. The day these issues dissapear, sure, you could optimize air traffic "perfectly". Until then, there is a reason ATC has not yet been replaced by computers.

For one thing, despite hugely complex mathematical models running 24/7 on massive supercomputers, we are unable to accurately predict the weather. An unexpected change in wind speed or direction at high altitude could result in an aircraft arriving several minutes earlier or later than expected. You would have no way of knowing in advance. Inevitably, even if your amazing mathematical model has spaced all the aircraft perfectly in advance, you are going to end up with two aircraft arriving on top of each other and having to deal with that on short notice.


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How to calculate the inaccuracy in the "standard" turn radius equation, for supersonic airspeeds
I learned to calculate the radius of a level turn (r) using the function $ r = \frac{V^2} {g   .  tan(bank angle)}$. V is true airspeed, g is the local gravity constant.
But now I have seen in the comments (from DeltaLima) to the answer (by Peter Kämpf), to a similar question How to calculate angular velocity and radius of a turn? that at very high speed, this equation underestimates the radius, because at such speeds, "your apparent weight is less". In the comments, the author states that for Mach 6,

the weight is about 10% less, so the radius is about 10% bigger if travelling eastwards at Mach 6 above the equator.

So at Mach 6 there is a 10% inaccuracy in the formula. How would I go about evaluating the inaccuracy at various Mach speeds, particularly between Mach 1 and Mach 6?

Some assumptions were made for this formula, not including the rotation speed of the earth and the rotational speed of the aircraft around the earth. The first term would be influenced by the position and heading you are having on earth. The second Term would be influenced by the Mach number adding an additional centrifugal force (the aircraft, becoming a satellite around the earth [As far as I remember this influence is only particularly interesting starting from Ma=3]).
Ignoring the first term you can just add an additional Term to the Equilibrium of Forces (previous Answer) in the opposite direction of m*g ("becoming lighter") and do the same procedure. Additional Force: $mV^2/R$ with $V$ the Ground Speed and with $R$ the distance of the aircraft from the center of earth -> R = r+alt (radius of earth + altitude).

If you’re travelling westwards then the aircraft’s weight will initially increase with increasing speed until the groundspeed equals that of the Earth’s rotation.  During a turn, the effective weight will therefore vary continuously as the aircraft turns.

The usual terminology does include the effect of rotation of Earth in the term gravity, though most calculations do just take the average value of $9.81 \frac{\mathrm{m}}{\mathrm{s}^2}$ instead of taking latitude into account and varying the value from $9.78$ at the equator to $9.83$ at the poles.


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What is the use of Stub Wings on Helicopters?
Some Helicopters like Russian Mi-24, UH-60 etx have Stub Wings. What is the role of such wings?
Russian Mi-24

UH-60

for those two I'd guess providing hard-points for the weapons and winches attached to them.

Can you possibly provide attribution for the images, e.g. the source?

Source : Google Images

@DamalaniSingh generally, "Google Images" is a collection of images from all over the web. For future reference, it's nice to include the source from which GI got the image.

In addition to serving as support for weapons, we must have in mind that they're both quite fast for a helicopter - 335 km/h (208 mph) for Mi and 294 km/h (183 mph) for UH. At such speeds, even small wings yield considerable aerodynamic effects, just like in planes. From Wikipedia article we can learn that the Mi's wings can provide up to 25% of total lift at speed and important stability to counter its tendency to Dutch Roll.
Curiously, both mentioned platforms exist in wingless configuration. For UH-60 it's quite common, while Mi-24 had its wings removed for breaking records. This hints that Mi-24 is much more dependent on its wings than UH-60.

Dutch Roll, for those unfamiliar with the term, is a "stable instability" that is common in heavier high-wing aircraft, including rotary wings. By adding aerodynamic wing stubs low on the fuselage, the imbalances that cause the roll are cancelled out.

What kind of records? Do you have any source? I think that for speed records the wings are quite advantageous.

@ROIMaison Expectably, time-to-climb record.

They're used for hanging munitions, external stores, etc. on. You can see in the picture of the Mi-24 that it has several rocket pods attached. They're referred to as "hardpoints" or "pylons".
I'm guessing that the reasons the pylons hang down from horizontal wings, rather than being attached more directly to the helicopter include:

Compatibility with existing airplane-based systems.
Moves rocket exhaust away from the body of the helicopter.
There's not enough room under the helicopter to hang them there.

Plus for quite some stuff you might want a way for visual inspection from within the cockpit.

all_licenses: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/3.0/


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Why this huge discrepancy in flight times?
I was looking at return flights from London - Azores islands and was astonished to see the huge difference in flight times, both flights are via Ryanair:
out: 3 hr 5 min
return: 4 hr 45 min

I am aware of differences due to wind conditions/jet streams and routes etc but for the return flight to take >50% longer really surprised me. What is likely to be the cause of this?

Not a bad deal - the direct flight is cheaper than one with stops.

TL;DR Probably "Operational" reasons

I would hazard a guess that this is a combination of a few factors

A longer route flown inbound to London
Flying in to a busy airspace like London requiring particular routing, particularly oft requiring length hold patterns
The time of day the flight in to London arrives being particularly busy (late afternoon/early evening)

These three factors may cause the airline to list the flight duration as longer than it would usually, in order to account for the possibility of a lengthy flight time.
If you look at the track of the outbound flight and compare it to the inbound flight you see that, at least on that occasion, a much longer track was followed. The airline may know that the route back to London is longer (for whatever reason) and adjust expected flight times accordingly.
Also, when you compare it to the only other direct flight departing and returning to the same airport (LGW) on skyscanner for the same route, the time difference is much less (15 minutes difference) which is much more usual. It may well be that the route to/from LGW is more equal outbound/return than the route taken to STN. It may also be that this flight in to LGW is at a typically quieter time of day.

The different flights can be done by different planes with different average speeds. Also the return flyght can get a (not show refuelling?) stop

Ryanair fleet is entirely 737-800s